Contents


NAME

     spbtrf - compute the Cholesky factorization of a  real  sym-
     metric positive definite band matrix A

SYNOPSIS

     SUBROUTINE SPBTRF(UPLO, N, KD, A, LDA, INFO)

     CHARACTER * 1 UPLO
     INTEGER N, KD, LDA, INFO
     REAL A(LDA,*)

     SUBROUTINE SPBTRF_64(UPLO, N, KD, A, LDA, INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 N, KD, LDA, INFO
     REAL A(LDA,*)

  F95 INTERFACE
     SUBROUTINE PBTRF(UPLO, [N], KD, A, [LDA], [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER :: N, KD, LDA, INFO
     REAL, DIMENSION(:,:) :: A

     SUBROUTINE PBTRF_64(UPLO, [N], KD, A, [LDA], [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER(8) :: N, KD, LDA, INFO
     REAL, DIMENSION(:,:) :: A

  C INTERFACE
     #include <sunperf.h>

     void spbtrf(char uplo, int n, int kd, float *a, int lda, int
               *info);

     void spbtrf_64(char uplo, long n, long kd,  float  *a,  long
               lda, long *info);

PURPOSE

     spbtrf computes the Cholesky factorization of  a  real  sym-
     metric positive definite band matrix A.

     The factorization has the form
        A = U**T * U,  if UPLO = 'U', or
        A = L  * L**T,  if UPLO = 'L',
     where U is an upper triangular matrix and L  is  lower  tri-
     angular.

ARGUMENTS

     UPLO (input)
               = 'U':  Upper triangle of A is stored;
               = 'L':  Lower triangle of A is stored.

     N (input) The order of the matrix A.  N >= 0.

     KD (input)
               The number of superdiagonals of the  matrix  A  if
               UPLO  = 'U', or the number of subdiagonals if UPLO
               = 'L'.  KD >= 0.

     A (input/output)
               On entry, the upper or lower triangle of the  sym-
               metric  band  matrix  A,  stored in the first KD+1
               rows of the array.  The j-th column of A is stored
               in  the j-th column of the array A as follows:  if
               UPLO = 'U', A(kd+1+i-j,j) =  A(i,j)  for  max(1,j-
               kd)<=i<=j;  if  UPLO = 'L', A(1+i-j,j)    = A(i,j)
               for j<=i<=min(n,j+kd).

               On exit, if INFO = 0, the triangular factor U or L
               from  the Cholesky factorization A = U**T*U or A =
               L*L**T of the band matrix A, in the  same  storage
               format as A.

     LDA (input)
               The leading dimension of  the  array  A.   LDA  >=
               KD+1.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, the leading minor of order i is
               not positive definite, and the factorization could
               not be completed.

FURTHER DETAILS

     The band storage scheme  is  illustrated  by  the  following
     example, when N = 6, KD = 2, and UPLO = 'U':
     On entry:                       On exit:

         *    *   a13  a24  a35  a46      *    *   u13  u24   u35
     u46
         *   a12  a23  a34  a45  a56      *   u12  u23  u34   u45
     u56
        a11  a22  a33  a44  a55  a66     u11  u22  u33  u44   u55
     u66

     Similarly, if UPLO = 'L' the format of A is as follows:

     On entry:                       On exit:

        a11  a22  a33  a44  a55  a66     l11  l22  l33  l44   l55
     l66
        a21  a32  a43  a54  a65   *      l21  l32  l43  l54   l65
     *
        a31  a42  a53  a64   *    *      l31  l42  l53   l64    *
     *

     Array elements marked * are not used by the routine.

     Contributed by
     Peter Mayes and Giuseppe Radicati, IBM  ECSEC,  Rome,  March
     23, 1989